Landfall

October 27th, 2012, 8:00am by Sam Wang

In Princeton, we’re making sure we have bottled water and other supplies. It’s not clear how serious Hurricane Sandy will be. But we are grateful for the advance warning that is made possible by the National Weather Service.

Seeing as how predictions are so useful, Andrew Ferguson and I have decided to put the Obama re-elect probability in the topline. We give two probabilities, which are built on the same assumptions that went into calculating the “strike zones” in the history graph. The “Random Drift” number is a minimum (conservative) probability, and the “Bayesian Prediction” is my best shot at calculating the actual win probability. In the coming 10 days, the two numbers will converge.

I will list the assumptions again. This will make the most sense if you know a little about what we do here at the Princeton Election Consortium.

Starting from a snapshot of today

Both predictions (“random drift” and “prediction”) start from a current snapshot of polling conditions, the Meta-Analysis of State Polls which forms the core of this site. The snapshot is listed in the top line above. It is currently Obama 297 EV, Romney 241 EV, Meta-margin Obama +1.96%. This predicts what would happen in an election held today.

To calculate this snapshot, we (a) use recent polls for each state (3 polls or 7 days, whichever is greater) to calculate the probability that one candidate is ahead, (b) calculate the exact distribution of all 2^51 = 2.3 quadrillion outcomes, measured in terms of electoral votes (EV), and (c) take the median of the distribution to get an expected outcome.

In addition, we calculate the amount by which polls must swing overall to create a perfect toss-up. This quantity is just like a two-candidate margin that people are used to seeing in polls, so we call it the Meta-Margin. Both the EV estimator and Meta-Margin are extremely precise, and performed very well on Election Eve in 2004 and 2008.

Projecting into the future

Between now and Election Day, opinion may move toward Obama or toward Romney. But by how much? To turn the snapshot into a prediction, we have to estimate how much movement may occur. There are two ways to do so. I have explained these before (“The Presidential predictor sharpens,” September 29). Here is how they fit into what’s listed above.

Random drift. Using past races, I have estimated how much the Meta-Margin is likely to fluctuates over time. In this “random drift” model, I assume that opinion is equally likely to move in either direction. (Nerds: at N days before the election, the drift has a standard deviation of 0.4% * sqrt(N).) If the Meta-Margin stays above zero, then Obama wins. Today, the probability of an Obama win is 89%.

Bayesian prediction. Here I make an additional assumption, that the final outcome is likely to be drawn from the values that the Meta-Margin has explored this year. This is equivalent to the idea that the Meta-Margin is more likely to move towards its average (Obama +3.1+/-1.3%) than away from it. This has been the case in past elections. In statistics this is called a “Bayesian prior,” as in prior assumption. Today, including that prior gives a win probability of 97%.

The prior is also used to calculate the red and yellow “strike zones” in the history graph.

In my view, the prediction is the correct probability. But if the prior seems like an unwarranted assumption to you, then use the Random Drift probability instead. This is a more conservative estimate. Anyway, over the coming days these probabilities will converge to the same value.

181 Comments so far ↓

What an amazing site this is. I cannot tell you the number of days I have flipped around the morning shows, wishing there was someplace to evaluate and discuss ACTUAL FREAKING DATA instead of spin, uncertainty, and doubt. 2/3 of what is discussed sails right over my head, which is awesome.

What I find most amazing is the tenuousness of Ohio. Romney has led in 9 of the 80 or so polls run since spring. I can’t figure out if this statistic, or the polls, or the % Silver gives it going to O, is comforting or meaningless.

Also, I cannot figure out the fascination with the National Tracking polls. As someone who knows nothing about the polling analysis business, if the consensus that this metric is inherently prone to noise, and therefore somewhat unreliable? In addition to being meaningless.

Ohio newspaper poll has the race tied in OH at 49-49. That’s a very good poll for the state, the gold standard. I think they may have punted, though. Anyways, it’s kindof stale (mostly pre-third debate) and will roll off Tuesday. We’ll see what PPP says tomorrow… yikes!

Robert Wright resurrects the “undecideds break to the challenger” canard, citing Bob Krumm’s analysis of 2004 as evidence. The difference between this version of the argument and the one that tripped up Prof. Wang is that Krumm claims the big break is visible over the course of the final week:

But in an addendum, he links to a new post by John Sides and an older one by Nate Silver expressing skepticism about the rule. Silver compiled data on all elections since 1968 and found no strong evidence for a consistent effect.

…though Silver’s data look spookier if you concentrate on true incumbent candidates, though he suggests it’s only because the challenger often trails by a lot, and there seems to be regression to the mean.

What I find more convincing is Silver’s recent article historically testing the reliability of state polling. That suggests no pattern of a break toward the challenger in the last weeks, though it does also suggest not placing much credence in state leads under about 1.5%.

All of that is factually true. However, that is probably not a great reason to discount that poll. There is little evidence that much has changed since the 3rd debate. The best way to think of it is this — it is one of many polls (even one of many credible polls). Even the best among them have many possible sources of error. That is why PEC takes the median, which as of today is Obama +2. Stay calm. Stick with the model (or at least a model).

It strikes me that there must be an upper and lower limit within which the MM moves under the random drift model, and in an election where the number of undecideds is low compared with previous elections, the range between the upper and lower limits would be very narrow and get narrower closer to the election.

If that’s correct then as the MM for the leading candidate approaches the upper limit, it seems that opinion would be more likely to move toward the lower limit than it is to rise to and above the upper limit. In other words, the “assum[ption] that opinion is equally likely to move in either direction” is incorrect.

The probability distribution is starting to get that “NMR spectrum” quality again, associated with lots of state leads firming up. I’d like the centroid to be higher than it is, but at least the uncertainties are less crazy-making.

The update included the WaPo O+4 but not the Gravis, at lest from what is posted on Pollster. But as far as the model is concerned, the VA results are perfectly balanced, not only for the pool of polls as a whole, but miraculously for each and every polling date in the last week:

When the Gravis poll gets into the data the 10/18 polls will drop out and we’ll have 3 polls showing Obama leading, 3 polls showing Romney leading, and 3 polls showing a tie. Get used to VA being tied.

DrOrbit, MN went from O+8 to O+5, NC went from R+3 to R+1, and WI moved from O+3.5 to O+2.

I agree with bsk (below) that the WI move looks wrong. Rather than dropping, by my reckoning WI should have moved up to O+5. So unless I’m mistaken, the MM should have increased rather than decreased.

That said, I fully expect the MM to bounce around a lot in the coming days. If it gets below 1% and stays there I’ll start worrying, and if it gets above 2% and stays there I’ll breathe easier. But moves up and down in the current range are nothing to get excited about.

There’s no reason I can see for the change in CO. Nothing new on Pollster, and O+3 looks correct. I’ve seen glitches like this appear in one update, and disappear in the next, without any apparent reason. This is another reason not to get worried about each up and down move in the MM.